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A145279
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Fecundity of Fibonacci numbers
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1
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0, 10, 10, 9, 9, 1, 7, 7, 5, 2, 1, 3, 1, 5, 8, 0, 5, 2, 1, 3, 1, 0, 1, 1, 7, 0, 2, 3, 3, 5, 0, 1, 0, 5, 0, 1, 0, 5, 0, 1, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 2, 1, 3, 5, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Subset of A070562. After the 184th Fibonacci number 127127879743834334146972278486287885163 the fecundity is equal to zero.
The indices of Fibonacci numbers whose fecundity are not zero are: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 22, 23, 24, 26, 27, 28, 29, 31, 33, 35, 37, 39, 42, 43, 53, 54, 55, 56, 57, 58, 78, 80, 85, 87, 97, 125, 184}. [From Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 27 2010]
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EXAMPLE
| Fib(6)=8 -> 8+8=16 -> 16+1*6=22 -> 22+2*2=26 -> 26+2*6=38 -> 38+3*8=62 -> 62+6*2=74 -> 74+7*4=102 -> 7 steps to reach a zero digit.
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MAPLE
| P:=proc(i) local a, b, c, d, f, g, ok, k, w, n; d:=0; f:=1; print(d); print(10); for n from 0 by 1 to i do a:=d+f; g:=f; f:=a; d:=g; b:=1; c:=0; ok:=1; while ok=1 do k:=a; w:=1; while k>0 do w:=w*(k-(trunc(k/10)*10)); k:=trunc(k/10); od; if w=0 then ok:=0; else c:=c+1; a:=a+w; fi; od; print(c); od; end: P(200);
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MATHEMATICA
| f[n_] := Length@ FixedPointList[ # + Times @@ IntegerDigits@# &, n] - 2; Array[f@ Fibonacci@# &, 105, 0] [From Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 27 2010]
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CROSSREFS
| A070562, A145280
Sequence in context: A112120 A099401 A087028 * A103708 A131722 A072803
Adjacent sequences: A145276 A145277 A145278 * A145280 A145281 A145282
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KEYWORD
| easy,nonn,base
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AUTHOR
| Paolo P. Lava & Giorgio Balzarotti (paoloplava(AT)gmail.com), Oct 06 2008
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